5x(x+4)=(4x+2)(x+4)

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Solution for 5x(x+4)=(4x+2)(x+4) equation: 


Simplifying
5x(x + 4) = (4x + 2)(x + 4)

Reorder the terms:
5x(4 + x) = (4x + 2)(x + 4)
(4 * 5x + x * 5x) = (4x + 2)(x + 4)
(20x + 5x2) = (4x + 2)(x + 4)

Reorder the terms:
20x + 5x2 = (2 + 4x)(x + 4)

Reorder the terms:
20x + 5x2 = (2 + 4x)(4 + x)

Multiply (2 + 4x) * (4 + x)
20x + 5x2 = (2(4 + x) + 4x * (4 + x))
20x + 5x2 = ((4 * 2 + x * 2) + 4x * (4 + x))
20x + 5x2 = ((8 + 2x) + 4x * (4 + x))
20x + 5x2 = (8 + 2x + (4 * 4x + x * 4x))
20x + 5x2 = (8 + 2x + (16x + 4x2))

Combine like terms: 2x + 16x = 18x
20x + 5x2 = (8 + 18x + 4x2)

Solving
20x + 5x2 = 8 + 18x + 4x2

Solving for variable 'x'.

Reorder the terms:
-8 + 20x + -18x + 5x2 + -4x2 = 8 + 18x + 4x2 + -8 + -18x + -4x2

Combine like terms: 20x + -18x = 2x
-8 + 2x + 5x2 + -4x2 = 8 + 18x + 4x2 + -8 + -18x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-8 + 2x + 1x2 = 8 + 18x + 4x2 + -8 + -18x + -4x2

Reorder the terms:
-8 + 2x + 1x2 = 8 + -8 + 18x + -18x + 4x2 + -4x2

Combine like terms: 8 + -8 = 0
-8 + 2x + 1x2 = 0 + 18x + -18x + 4x2 + -4x2
-8 + 2x + 1x2 = 18x + -18x + 4x2 + -4x2

Combine like terms: 18x + -18x = 0
-8 + 2x + 1x2 = 0 + 4x2 + -4x2
-8 + 2x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + 2x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}

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